At the domain boundary, perform a fourth-order extrapolation of cell-averaged interior data to fill two layers of ghost cells (we assume an exchange will be performed elsewhere to fill interior ghost cells). Among other possible uses, this enables the fourthOrderCellToFace utility to then be called without worrying about boundaries.

Perform a second-order extrapolation of a_data values in a_srcbox to set the values of a_data in the adjacent width-one boxes on the low and high sides of a_srcbox. The extrapolation is only performed if the adjacent width-one boxes lie outside the domain box (i.e., are physical boundary ghost cells).

Perform a second-order extrapolation of the input a_data from the a_srcbox box to adjacent destination boxes of width one on the low and high sides of srcbox in the directions transverse to a_dir. This can be used, for example, to fill ghost cells prior to computing the transverse gradients (relative to the a_dir direction) on cell faces via the product formula (for computing the fourth-order average of a product in terms of the averages of each factor).

Perform a second-order extrapolation of the input a_data from the a_interiorbox box to adjacent destination boxes of width one on the low and high sides of a_interiorbox in the directions transverse to dir. The extrapolation is only performed if the adjacent width-one boxes lie outside the domain box (i.e., are physical boundary ghost cells). This can be used to fill ghost cells prior to computing the transverse gradients (relative to the a_dir direction) on cell faces via the product formula (for computing the fourth-order average of a product in terms of the averages of each factor).

Perform a second-order extrapolation of the input a_data from faces of a_interiorbox to adjacent destination boxes of width one on the low and high sides of a_interiorbox in the directions transverse to dir. The extrapolation is only performed if the adjacent width-one boxes lie outside the domain box (i.e., are physical boundary ghost faces).

Perform a zeroth-order extrapolation of a_data values in a_srcbox to set the values of a_data in the adjacent width-one boxes on the low and high sides of a_srcbox. The extrapolation is only performed if the adjacent width-one boxes lie outside the domain box (i.e., are physical boundary ghost cells).